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Find the value of \(\cos(60° + 45°)\) leaving your answer in surd form.

Further Mathematics
WAEC 2010

Find the value of \(\cos(60° + 45°)\) leaving your answer in surd form.

  • A. \(\frac{6 + \sqrt{2}}{4}\)
  • B. \(\frac{3 + \sqrt{6}}{4}\)
  • C. \(\frac{\sqrt{2} - \sqrt{6}}{4}\)
  • D. \(\frac{3 - \sqrt{6}}{4}\)
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Correct Answer: Option C
Explanation

\(\cos (x + y) = \cos x \cos y - \sin x \sin y \)

\(\cos (60 + 45) = \cos 60 \cos 45 - \sin 60 \sin 45\)

= \(\frac{1}{2} \times \frac{\sqrt{2}}{2} - \frac{\sqrt{3}}{2} \times \frac{\sqrt{2}}{2}\)

= \(\frac{\sqrt{2} - \sqrt{6}}{4}\)


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